I am going to use an example raid with 4 bosses for simplicity. Paralleling your example:Player1 joins a fresh raid, kills the first boss. The raid falls apart so he joins an already in progress raid whom are on the 4th boss.

If the raid is already inside waiting for him to enter, will he be able to enter and start with them on the 4th boss? or will it stop him from entering until bosses 2 & 3 are killed?

Yes, he will be able to enter and kill the 4th boss.Loot is per-player, we don’t see any point in locking someone to some sort of raid-id. However, if that same group decides to queue for a new instance, any bosses that anyone in that group has not already killed, will spawn again.

And if it doesn't stop him from entering, would leaving the instance or soft resetting the instance spawn bosses 2 & 3?

There’s no soft resetting because it’s a queue system. If they queue again for a new instance, then yes, the bosses will spawn again.